1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various countries \(m\) of the world. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was c62ef5b7f851ac4b58c3379b5c71b76a3e9e50b5.

2 Data

Data are downloaded from [3]. Minor formatting is applied to get the data ready for further processing.

3 Basic Exploration

Below we plot cumulative case count on a log scale by continent. Note that “Other” relates to ships.

Reported Cases by Continent

Reported Cases by Continent

Below we plot the cumulative deaths by country on a log scale:

Reported Deaths by Continent

Reported Deaths by Continent

4 Method & Assumptions

The methodology is described in detail here.

Countries with populations of less than 500 000 are excluded.

5 Results

5.1 World-wide

Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
cases 4,081,632 2021-01-26 0.9 0.9 0.9
deaths 100,499 2021-01-26 1.0 1.0 1.0

5.2 Current reproduction number estimates by country

Below current (last weekly) \(R_{t,m}\) estimates are plotted on a world map.

5.2.0.1 Cases

5.2.1 Deaths

5.3 Top 10 countries

Below we show various extremes of \(R_{t,m}\) where counts (deaths or cases) exceed 50 in the last week.

5.3.1 Lowest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Palestine deaths 62 2021-01-26 0.5 0.7 0.9
South Korea deaths 78 2021-01-26 0.6 0.7 0.9
Nigeria deaths 58 2021-01-26 0.5 0.7 0.9
Guatemala deaths 173 2021-01-26 0.6 0.7 0.9
Canada deaths 692 2021-01-26 0.7 0.7 0.8
Germany deaths 4,622 2021-01-26 0.8 0.8 0.8
Morocco deaths 176 2021-01-26 0.7 0.8 0.9
Azerbaijan deaths 68 2021-01-26 0.6 0.8 1.0
Bosnia and Herzegovina deaths 112 2021-01-26 0.7 0.8 1.0
Jordan deaths 78 2021-01-26 0.7 0.9 1.1

5.3.2 Lowest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Sudan cases 72 2021-01-26 0.1 0.1 0.2
Congo cases 178 2021-01-26 0.3 0.5 0.7
Eritrea cases 93 2021-01-26 0.4 0.6 0.8
Ireland cases 13,012 2021-01-26 0.6 0.7 0.7
Armenia cases 1,320 2021-01-26 0.6 0.7 0.7
Zimbabwe cases 3,329 2021-01-26 0.7 0.7 0.7
Trinidad and Tobago cases 81 2021-01-26 0.6 0.7 0.9
Cyprus cases 958 2021-01-26 0.7 0.7 0.8
South Africa cases 66,862 2021-01-26 0.7 0.8 0.8
Ukraine cases 31,685 2021-01-26 0.7 0.8 0.8

5.3.3 Highest \(R_{t,m}\) based on deaths

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Sudan deaths 147 2021-01-26 2.2 3.1 4.3
Kazakhstan deaths 141 2021-01-26 1.9 2.3 2.8
Peru deaths 1,337 2021-01-26 2.0 2.2 2.3
Dominican Republic deaths 103 2021-01-26 1.5 1.9 2.5
Mozambique deaths 110 2021-01-26 1.4 1.7 2.1
Malawi deaths 204 2021-01-26 1.3 1.6 1.9
Kosovo deaths 55 2021-01-26 1.1 1.4 1.9
Spain deaths 2,621 2021-01-26 1.3 1.4 1.5
Portugal deaths 1,766 2021-01-26 1.3 1.4 1.5
Bolivia deaths 383 2021-01-26 1.2 1.3 1.5

5.3.4 Highest \(R_{t,m}\) based on cases

Country Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
Cameroon cases 1,607 2021-01-26 1.4 1.7 2.2
Ghana cases 3,704 2021-01-26 1.4 1.6 1.8
Peru cases 46,672 2021-01-26 1.6 1.6 1.6
Equatorial Guinea cases 89 2021-01-26 1.2 1.5 1.9
Madagascar cases 442 2021-01-26 1.3 1.4 1.6
Maldives cases 614 2021-01-26 1.3 1.4 1.5
Benin cases 230 2021-01-26 1.1 1.4 1.7
Thailand cases 1,993 2021-01-26 1.2 1.3 1.4
Rwanda cases 2,337 2021-01-26 1.3 1.3 1.4
Cote d’Ivoire cases 1,854 2021-01-26 1.2 1.3 1.5

5.4 Risk Quadrants

The plots below show weekly cases (or deaths) on the X-axis and the reproduction number on the Y-axis. By dividing this into 4 quadrants we can identify countries with high cases and high reproduction numbers, or high cases and low reproduction numbers etc.

Values where the reproduction number exceeds 3 are plotted at 3.

5.4.1 Cases

Risk Quadrants - Cases

5.4.2 Deaths

Risk Quadrants - Deaths

5.5 Country Plots by Continent

Below we plot results for each country/province in a list. Values larger than 3 are plotted at 3.

5.5.1 Africa

5.5.1.1 Algeria

5.5.1.2 Angola

5.5.1.3 Benin

5.5.1.4 Botswana

5.5.1.5 Burkina Faso

5.5.1.6 Burundi

5.5.1.7 Cameroon

5.5.1.8 Cape Verde

5.5.1.9 Central African Republic

5.5.1.10 Chad

5.5.1.11 Comoros

5.5.1.12 Congo

5.5.1.13 Cote d’Ivoire

5.5.1.14 Democratic Republic of Congo

5.5.1.15 Djibouti

5.5.1.16 Egypt

5.5.1.17 Equatorial Guinea

5.5.1.18 Eritrea

5.5.1.19 Eswatini

5.5.1.20 Ethiopia

5.5.1.21 Gabon

5.5.1.22 Gambia

5.5.1.23 Ghana

5.5.1.24 Guinea

5.5.1.25 Guinea-Bissau

5.5.1.26 Kenya

5.5.1.27 Lesotho

5.5.1.28 Liberia

5.5.1.29 Libya

5.5.1.30 Madagascar

5.5.1.31 Malawi

5.5.1.32 Mali

5.5.1.33 Mauritania

5.5.1.34 Mauritius

5.5.1.35 Morocco

5.5.1.36 Mozambique

5.5.1.37 Namibia

5.5.1.38 Niger

5.5.1.39 Nigeria

5.5.1.40 Rwanda

5.5.1.41 Senegal

5.5.1.42 Sierra Leone

5.5.1.43 Somalia

5.5.1.44 South Africa

5.5.1.45 South Sudan

5.5.1.46 Sudan

5.5.1.47 Togo

5.5.1.48 Tunisia

5.5.1.49 Uganda

5.5.1.50 Zambia

5.5.1.51 Zimbabwe

5.5.2 Asia

5.5.2.1 Afghanistan

5.5.2.2 Armenia

5.5.2.3 Azerbaijan

5.5.2.4 Bahrain

5.5.2.5 Bangladesh

5.5.2.6 Bhutan

5.5.2.7 Cambodia

5.5.2.8 China

5.5.2.9 Georgia

5.5.2.10 India

5.5.2.11 Indonesia

5.5.2.12 Iran

5.5.2.13 Iraq

5.5.2.14 Israel

5.5.2.15 Japan

5.5.2.16 Jordan

5.5.2.17 Kazakhstan

5.5.2.18 Kuwait

5.5.2.19 Kyrgyzstan

5.5.2.20 Lebanon

5.5.2.21 Malaysia

5.5.2.22 Maldives

5.5.2.23 Mongolia

5.5.2.24 Myanmar

5.5.2.25 Nepal

5.5.2.26 Oman

5.5.2.27 Pakistan

5.5.2.28 Palestine

5.5.2.29 Philippines

5.5.2.30 Qatar

5.5.2.31 Saudi Arabia

5.5.2.32 Singapore

5.5.2.33 South Korea

5.5.2.34 Sri Lanka

5.5.2.35 Syria

5.5.2.36 Taiwan

5.5.2.37 Tajikistan

5.5.2.38 Thailand

5.5.2.39 Turkey

5.5.2.40 United Arab Emirates

5.5.2.41 Uzbekistan

5.5.2.42 Vietnam

5.5.2.43 Yemen

5.5.3 Europe

5.5.3.1 Albania

5.5.3.2 Austria

5.5.3.3 Belarus

5.5.3.4 Belgium

5.5.3.5 Bosnia and Herzegovina

5.5.3.6 Bulgaria

5.5.3.7 Croatia

5.5.3.8 Cyprus

5.5.3.9 Czechia

5.5.3.10 Denmark

5.5.3.11 Estonia

5.5.3.12 Finland

5.5.3.13 France

5.5.3.14 Germany

5.5.3.15 Greece

5.5.3.16 Hungary

5.5.3.17 Ireland

5.5.3.18 Italy

5.5.3.19 Kosovo

5.5.3.20 Latvia

5.5.3.21 Lithuania

5.5.3.22 Luxembourg

5.5.3.23 Moldova

5.5.3.24 Montenegro

5.5.3.25 Netherlands

5.5.3.26 North Macedonia

5.5.3.27 Norway

5.5.3.28 Poland

5.5.3.29 Portugal

5.5.3.30 Romania

5.5.3.31 Russia

5.5.3.32 Serbia

5.5.3.33 Slovakia

5.5.3.34 Slovenia

5.5.3.35 Spain

5.5.3.36 Sweden

5.5.3.37 Switzerland

5.5.3.38 Ukraine

5.5.3.39 United Kingdom

5.5.4 North America

5.5.4.1 Canada

5.5.4.2 Costa Rica

5.5.4.3 Cuba

5.5.4.4 Dominican Republic

5.5.4.5 El Salvador

5.5.4.6 Guatemala

5.5.4.7 Haiti

5.5.4.8 Honduras

5.5.4.9 Jamaica

5.5.4.10 Mexico

5.5.4.11 Nicaragua

5.5.4.12 Panama

5.5.4.13 Trinidad and Tobago

5.5.4.14 United States

5.5.5 Oceania

5.5.5.1 Australia

5.5.5.2 New Zealand

5.5.5.3 Papua New Guinea

5.5.6 South America

5.5.6.1 Argentina

5.5.6.2 Bolivia

5.5.6.3 Brazil

5.5.6.4 Chile

5.5.6.5 Colombia

5.5.6.6 Ecuador

5.5.6.7 Guyana

5.5.6.8 Paraguay

5.5.6.9 Peru

5.5.6.10 Suriname

5.5.6.11 Uruguay

5.5.6.12 Venezuela

5.6 Detailed Output

Detailed output for all countries are saved to a comma-separated value file. The file can be found here.

6 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

7 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim

[3] M. Roser, H. Ritchie, E. Ortiz-Ospina, and J. Hasell, “Coronavirus pandemic (COVID-19),” Our World in Data, 2020 [Online]. Available: https://ourworldindata.org/coronavirus. [Accessed: 17-Dec-2020]